Some applications require estimation of the fundamental angular frequency and extraction of a clean balanced three-phase sinusoidal signal, i.e. the fundamental positive sequence component, from a reference signal, which may be subject to severe unbalance and high harmonic distortion. For example, this is the case in connection with the synchronization of three-phase grid-connected systems, such as power conditioning equipment, flexible ac transmission systems (FACTS) [2]-[3], power line conditioners, regenerative drives, uninterruptible power supplies (UPS) [4]-[5], grid-connected inverters for alternative energy sources, and other distributed generation and storage systems.
The most extended technique used for frequency-insensitive positive-sequence detection is the conventional three-phase phase-locked loop (PLL) based on the synchronous reference frame (SRF-PLL) [6], see also [1] for a complete review of conventional schemes. Different schemes have been disclosed based on this conventional scheme [7]-[11]. Like many other schemes, the SRF-PLL relays in a linearization assumption, and thus, the results can only be guaranteed locally. Under ideal utility conditions, i.e. without harmonic distortion or unbalance, a relatively high bandwidth feedback loop of the SRF-PLL yields a fast and precise detection of the phase angle and amplitude of the reference signal. However, most of the schemes based on the SRF-PLL approach are very sensitive to harmonic distortion [12]-[13].
If the reference signal is distorted with low-order harmonics, i.e. harmonics close to the fundamental frequency, the bandwidth of the SRF-PLL feedback loop can be reduced to reject and cancel out the effect of these harmonics on the output. However, the PLL bandwidth reduction is not an acceptable solution as its speed of response is reduced considerably as well. It should be understood that the problem of estimating this fundamental component gets even more challenging in the case of unbalanced signals [11], [14].